A) 124.5 cm
B) 144.5 cm
C) 65.0 cm
D) 99.0 cm
Correct Answer: D
Solution :
Given: Separation of lens for two of its position, d = 10 cm Ratio of size of the images in two positions \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{3}{2}\] Distance of object from the screen, D = ? Applying formula, \[\frac{{{I}_{1}}}{{{I}_{2}}}=\frac{{{(D+d)}^{2}}}{{{(D-d)}^{2}}}\] \[\Rightarrow \]\[\frac{3}{2}=\frac{{{(D+10)}^{2}}}{{{(D-10)}^{2}}}\]\[\Rightarrow \]\[\frac{3}{2}=\frac{{{D}^{2}}+100+20D}{{{D}^{2}}+100-20D}\] \[\Rightarrow \]\[3{{D}^{2}}+300-60D=2{{D}^{2}}+200+40D\] \[\Rightarrow \]\[{{D}^{2}}-100D+100=0\] On solving, we get D = 99 cm Hence the distance between the screen and the object is 99 cm.
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